Wow, lots of great questions here and none of them are easy. Let me take them one by one.
At what point do consultants start to specialise? Do they tend to specialise by function or industry (or both)?
Usually around their second year, but there is no rule, of course. For most it's rather an organic, natural process, rather than an intentional one. The most successful consultants I've met actually pursued a group of people that they wanted to work with, rather than a specific topic or industry. It's the people that will actually determine how much you're enjoying the job.
How does one maneuver to align themselves into their areas of interest rather than being pigeonholed into something that he/she just happen to have a lot of experience in?
In short, you learn to say ‘no’ and accept the consequences that come with that. It will be harder to get staffed in something you like and don't have experience in rather than something that you already know, but if you're consistent at it, over a longer period of time it will get easier and easier as you build your experience and network.
Is it possible that an individual could be an expert in areas that may not appear to have natural synergies? Eg. Strategy, Digital and Private Equity, Aerospace and FMCG. (Random example)
Yes. Funky combos can actually makes you more attractive for staffing.
Can individuals be part of one group and dotted lined to another groups? Or are they strictly defined buckets?
It depends on the firm, but they can usually have this dotted line. Practices and groups within firms are constantly re-organising, so it's not useful to think of them in terms of silos. The only thing to bear in mind is what are the expectations of each of these groups. Some practices, for instance, require that you do x% of your projects / staffing time within their area. So that's rather the metric to keep an eye on.
Also do you pick a mentor or are you assigned a mentor? How do you ensure you get a good mentor fit?
Usually you pick on. Find the people who inspire you and gradually get closer to them. You don't have to literally ask them to be your ‘mentor’. The point is rather to shadow them as much as possible, get staffed on their projects, ask for their advice and help, and help them in return whenever they need it. Mentorship is a two-way street.